Covid Trends
Jose Tamez
4/8/2020
Forcasting COVID-19 Deaths
A simple model for the estimation of the maximum percentage of deaths due to COVID-19.
NOTE: I’m not an epidiomiologist.
The prediction based on a simple logistic model and:
70% of SARS-CoV-2 exposure
10% Infection efficacy ie. 10% of the exposure subjects turns into a Covid-19 case
1% of Mortality
For each country we will use the urban population
I’ll estimate the death rates based on current trends fitted to the logistic function.
The last 14 days will be used for the peak estimations. Peak estimations will be done using:
- The last reported 14 observations
- 14 observations from the last week
- 14 observations ending two weeks ago
- 14 observations ending three weeks ago
- 14 observations ending four weeks ago
# The expetec % of deaths in each country
expectedtotalFatalities = 0.7*0.1*0.01
# The number of observations used for the trends
daysWindow <- 14
currentdate <- "April 7:" Loading the data
The data is the training set from: Kaggle: COVID19 Global Forecasting (Week 3)
https://www.kaggle.com/c/covid19-global-forecasting-week-3/data
train <- read.csv("~/GitHub/COVIDTrends/Kaggle/train.csv", stringsAsFactors=FALSE)
train$ProviceCountry <- paste(train$Country_Region,train$Province_State,sep=":")
train[train$Country_Region=="Korea, South","Country_Region"] <- "South Korea"
trainCountry <- train[train$Province_State == "",]
covid19_datapopulation <- read.csv("~/GitHub/COVIDTrends/Kaggle/covid19_data - population.csv", stringsAsFactors=FALSE)
rownames(covid19_datapopulation) <- paste(covid19_datapopulation$Country,":",sep="")
totalPoulation <- as.numeric(str_replace_all(covid19_datapopulation$Population_2020,",",""))
totalUrbanPoulation <- as.numeric(str_replace_all(covid19_datapopulation$Urban_pop_pct,"\\%",""))/100.0
totalUrbanPoulation[is.na(totalUrbanPoulation)] <- 1.0;
totalUrbanPoulation <- totalPoulation*totalUrbanPoulation
covid19_datapopulation$ExpectedFatalities <- expectedtotalFatalities*(
totalUrbanPoulation +
0.1*(totalPoulation-totalUrbanPoulation)
)
trainCountry$PerFatalities <- trainCountry$Fatalities/covid19_datapopulation[trainCountry$Country_Region,"ExpectedFatalities"]
trainCountry <- trainCountry[trainCountry$Fatalities > 0,]
expfatalities <- covid19_datapopulation$ExpectedFatalities/1.0e6
names(expfatalities) <- covid19_datapopulation$Country
expfatalities <- expfatalities[order(-expfatalities)]
plot.new()
op <- par(no.readonly = TRUE)
par(mar=c(8,4,4,4),pty="m")
#barplot(expfatalities[1:30],las=2,cex.names =0.70,cex.axis = 0.60,horiz = TRUE,main="Expected Fatalities",xlab="MIllions")
barplot(expfatalities[1:30],las=2,cex.names =0.70,cex.axis = 0.60,main="Expected Fatalities",ylab="Millions")
par(op)Ploting some trends
Country_Region <- names(table(trainCountry$Country_Region))
totaldeaths <- numeric()
for (ctr in Country_Region)
{
totaldeaths <- append(totaldeaths,max(trainCountry[trainCountry$Country_Region == ctr,"Fatalities"]))
}
names(totaldeaths) <- Country_Region
totaldeaths <- totaldeaths[order(-totaldeaths)]
plot(trainCountry[trainCountry$Country_Region == names(totaldeaths[1]),"Fatalities"],main="Fatalities",xlab="Days",ylab="Fatalities")
for (ctr in names(totaldeaths[1:25]))
{
linp <- trainCountry[trainCountry$Country_Region == ctr,"Fatalities"]
lines(linp)
text(length(linp)-1,linp[length(linp)],ctr)
}
plot(trainCountry[trainCountry$Country_Region == names(totaldeaths[1]),"PerFatalities"],main="% Fatalities",xlab="Days",ylab=" % Fatalities")
for (ctr in names(totaldeaths[1:25]))
{
linp <- trainCountry[trainCountry$Country_Region == ctr,"PerFatalities"]
lines(linp)
text(length(linp)-1,linp[length(linp)],ctr)
}
totaldeaths <- totaldeaths[totaldeaths > 100]Estimating the peaks
par(op)
cn = 20
par(mfrow=c(1,1),cex=0.65,mar=c(4,4,4,5))
for (cn in c(1:length(totaldeaths)))
{
endDay <- 0
countryNumber <- cn
mainName <- paste(currentdate,names(totaldeaths[countryNumber]))
datsetone <- trainCountry[trainCountry$Country_Region == names(totaldeaths[countryNumber]),"PerFatalities"]
datsetchange <- c(datsetone[1],datsetone[2:length(datsetone)]-datsetone[1:(length(datsetone)-1)])
lastobs <- length(datsetone)
datsetchange <- 0.35*datsetchange +
0.65*c(datsetone[1],0.5*(datsetone[3:lastobs]-datsetone[1:(length(datsetone)-2)]),datsetchange[lastobs])
datasetone <- as.data.frame(cbind(days=c(1:length(datsetone)),fatalities = datsetone,newfatalities = datsetchange))
numdays <- nrow(datasetone)
ndays <- max(c(numdays - endDay,7))
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
roestimate <- try(nls(fatalities ~ logisticcdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= -0.1,to=ndays),
control=list(warnOnly=TRUE)))
if (!inherits(roestimate, "try-error"))
{
smo <- summary(roestimate)
predictedTotalCases <- logisticcdf(c(1:120),smo$coefficients[1,1],smo$coefficients[2,1])
ymax <- max(c(predictedTotalCases,datasetone$fatalities))
plot(predictedTotalCases,ylim=c(0,1.0),type="l",lty=2,xlab="days",ylab="Fraction of the Total Expected Fatalities",main=mainName)
lines(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],lwd=5)
lines(datasetone$days[c(1:ndays)],10*datasetone$newfatalities[c(1:ndays)],lty=3,lwd=4,col=2)
daycode <- c("Last:","One Week Ago:","Two Weeks Ago:","Three Weeks Ago:")
dc <- 1
for (endDay in c(0,7,14,21,28))
{
ndays <- numdays - endDay
if (ndays > 7)
{
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
pdfestimate <- try(nls(newfatalities ~ logisticpdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= smo$coefficients[1,1],to=smo$coefficients[2,1]),
control=list(warnOnly=TRUE)))
if (!inherits(pdfestimate, "try-error"))
{
nsmo <- summary(pdfestimate)
newcases <- logisticpdf(c(1:120),nsmo$coefficients[1,1],nsmo$coefficients[2,1])
lines(10*newcases,lty=6,col=(endDay+7)/7,lwd= 1 + 1*(dc == 1))
dmax <- which.max(newcases)
daystopeak <- nsmo$coefficients[2,1]-numdays;
if (dc == 1)
{
text(dmax+7,10*max(newcases)+0.05,paste("Days to Peak:",sprintf("%3.0f",daystopeak)),cex=0.8)
}
}
}
dc <- dc + 1
}
}
else
{
plot(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],
ylim=c(0,1.0),
type="l",
lty=2,
xlab="days",
ylab="% Fatalities",
main=mainName)
}
legend("topright",
legend = c("Estimated","Observed","New Fatalities","Estimated New","One Week Ago","Two Weeks Ago","Three Weeks Ago","Four Weeks Ago"),
col = c(1,1,2,1,2,3,4,5),
lty = c(2,1,3,6,6,6,6,6),
lwd = c(1,5,4,2,1,1,1,1))
z <- c(0:10)/100;
axis(4, at=10*z,labels=round(z,digits=2),
col.axis="blue", las=2, cex.axis=0.7, tck=-.01)
mtext("Fraction of New Fatalities", cex=0.5,side=4, line=3, cex.lab=0.3, col="black",las=3)
}
Estimation by Province or State
trainProvince <- train[train$Province_State != "",]
#locations_population <- read.csv("~/GitHub/COVIDTrends/Kaggle/locations_population.csv", stringsAsFactors=FALSE)
library(readxl)
locations_population <- read_excel("Kaggle/locations_population.xlsx")
totalStatePoulation <- as.numeric(locations_population$UrabPop)
names(totalStatePoulation) <- locations_population$Province.State
totalStatePoulation <- totalStatePoulation[locations_population$Province.State != ""]
trainProvince$PerFatalities <- (trainProvince$Fatalities/totalStatePoulation[trainProvince$Province_State])/expectedtotalFatalities
trainProvince <- trainProvince[trainProvince$Fatalities > 0,]
Province_State <- names(table(trainProvince$Province_State))
totaldeaths <- numeric()
for (ctr in Province_State)
{
totaldeaths <- append(totaldeaths,max(trainProvince[trainProvince$Province_State == ctr,"Fatalities"]))
}
names(totaldeaths) <- Province_State
totaldeaths <- totaldeaths[order(-totaldeaths)]
totaldeaths <- totaldeaths[totaldeaths>100]Estimating the State/Province Peaks
par(op)
cn = 2
par(mfrow=c(1,1),cex=0.65,mar=c(4,4,4,5))
for (cn in c(1:length(totaldeaths)))
{
endDay <- 0
stateNumber <- cn
mainName <- paste(currentdate,names(totaldeaths[stateNumber]))
datsetone <- trainProvince[trainProvince$Province_State == names(totaldeaths[stateNumber]),"PerFatalities"]
datsetchange <- c(datsetone[1],datsetone[2:length(datsetone)]-datsetone[1:(length(datsetone)-1)])
lastobs <- length(datsetone)
datsetchange <- 0.35*datsetchange +
0.65*c(datsetone[1],0.5*(datsetone[3:lastobs]-datsetone[1:(length(datsetone)-2)]),datsetchange[lastobs])
datasetone <- as.data.frame(cbind(days=c(1:length(datsetone)),fatalities = datsetone,newfatalities = datsetchange))
numdays <- min(nrow(datasetone),which.max(datasetone$newfatalities)+7)
ndays <- max(c(numdays - endDay,7))
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
roestimate <- try(nls(fatalities ~ logisticcdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= -0.1,to=ndays),
control=list(warnOnly=TRUE)))
if (!inherits(roestimate, "try-error"))
{
smo <- summary(roestimate)
predictedTotalCases <- logisticcdf(c(1:120),smo$coefficients[1,1],smo$coefficients[2,1])
ymax <- max(c(predictedTotalCases,datasetone$fatalities))
plot(predictedTotalCases,ylim=c(0,1.0),type="l",lty=2,xlab="days",ylab="Fraction of the Total Expected Fatalities",main=mainName)
lines(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],lwd=5)
lines(datasetone$days[c(1:ndays)],10*datasetone$newfatalities[c(1:ndays)],lty=3,lwd=4,col=2)
daycode <- c("Last:","One Week Ago:","Two Weeks Ago:","Three Weeks Ago:")
dc <- 1
endDay <- 0;
for (endDay in c(0,7,14,21,28))
{
ndays <- numdays - endDay
if (ndays > 7)
{
startday <- max(1,ndays - daysWindow)
daysrange <- c(startday:ndays)
pdfestimate <- try(nls(newfatalities ~ logisticpdf(days, ro, to),
data = datasetone[daysrange,],
start=list(ro= smo$coefficients[1,1],to=smo$coefficients[2,1]),
control=list(warnOnly=TRUE)))
if (!inherits(pdfestimate, "try-error"))
{
nsmo <- summary(pdfestimate)
newcases <- logisticpdf(c(1:120),nsmo$coefficients[1,1],nsmo$coefficients[2,1])
lines(10*newcases,lty=6,col=(endDay+7)/7,lwd= 1 + 1*(dc == 1))
dmax <- which.max(newcases)
daystopeak <- nsmo$coefficients[2,1]-numdays;
if (dc == 1)
{
text(dmax+7,10*max(newcases)+0.05,paste("Days to Peak:",sprintf("%3.0f",daystopeak)),cex=0.8)
}
}
}
dc <- dc + 1
}
}
else
{
plot(datasetone$days[c(1:ndays)],datasetone$fatalities[c(1:ndays)],
ylim=c(0,1.0),
type="l",
lty=2,
xlab="days",
ylab="% Fatalities",
main=mainName)
}
legend("topright",
legend = c("Estimated","Observed","New Fatalities","Estimated New","One Week Ago","Two Weeks Ago","Three Weeks Ago","Four Weeks Ago"),
col = c(1,1,2,1,2,3,4,5),
lty = c(2,1,3,6,6,6,6,6),
lwd = c(1,5,4,2,1,1,1,1))
z <- c(0:10)/100;
axis(4, at=10*z,labels=round(z,digits=2),
col.axis="blue", las=2, cex.axis=0.7, tck=-.01)
mtext("Fraction of New Fatalities", cex=0.5,side=4, line=3, cex.lab=0.3, col="black",las=3)
}
